List of practice Questions

A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at $ t = 0 $ s is received back by the transceiver 100 ns (nanoseconds) later after reflection from the car. A second pulse emitted at $ t = 0.1 $ s is received back 90 ns later. Given the speed of light is $ 3 \times 10^8 $ m/s, the average speed of the car in this interval is _________

Given below are two statements:
Statement I: The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II: The rms speed of oxygen molecules in a gas is $v$ If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2 v$ In the light of the above statements, choose the correct answer from the options given below:

Consider a cylindrical tank of radius $1 m$ is filled with water. The top surface of water is at $15 m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5 m$ from the bottom. A force of $5 × 10^5 N$ is applied on the top surface of water using a piston. The speed of efflux from the hole will be:

(Given atmosphere pressure $P_A = 1.01 × 10^5 Pa$, density of water $ρ_w 1000 Kg/m^3$ and gravitational acceleration $g = 10 m/s^2$)

From a circular disc of radius $ R $, a square is cut out with a radius as its diagonal. The centre of mass of the remaining portion is at a distance (from the centre)

Let $X = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \\ \end{bmatrix}$,
Y = αI + βX + γX² and
Z = α²l - αβX + (β² - αϒ)X² ,α,β,ϒ ∈ R.
If $Y^{-1} = \begin{bmatrix} \frac{1}{5} & -\frac{2}{5} & \frac{1}{5} \\ 0 & \frac{1}{5} & -\frac{2}{5} \\ 0 & 0 & \frac{1}{5} \\ \end{bmatrix}$,
then ( α - β + ϒ )² is equal to ________.

If $\vec a= 2\hat i +\hat j + 3\hat k$, $\vec b = 3\hat i + 3\hat j + \hat k$ and $\vec c = c_1\hat i + c_2\hat j + c_3\hat k$ are coplanar vectors and $\vec a.\vec c = 5$, $\vec b⊥\vec c$ then $122( c_1 + c_2 + c_3 )$ is equal to _____ .

The area of the polygon, whose vertices are the non-real roots of the equation $\bar z = iz^2$ is

Match List-I with List-II.

List-I (Metal)	List-II (Emitted light wavelength (nm))
(A) Li	(I) 670.8
(B) Na	(II) 589.2
(C) Rb	(III) 780.0
(D) Cs	(IV) 455.5

Choose the most appropriate answer from the options given below:

Write the name of the process in Fischer Tropsch process in the synthesis of gasoline.

Identify the molecularity of following elementary reaction: NO(g) + O$_3$(g) $\to$ NO$_3$(g) + O(g)

The major product formed in the following reaction is

20 mL of 0.1 M NH₄OH is mixed with 40 mL of 0.05 M HCl.The pH of the mixture is nearest to:(Given: K_b(NH₄OH) = 1 × 10^–5,log 2 = 0.30,log 3 = 0.48, log 5 = 0.69, log 7 = 0.84, log 11 =1.04)

The series of positive multiples of 3 is divided into sets: {3}, {6, 9, 12}, {15, 18, 21, 24, 27},…… Then the sum of the elements in the 11^th set is equal to ________.

Let $y = y(x)$ be the solution of the differential equation $(1 - x^2) \, dy = (xy + (x^3 + 2) \sqrt{1 - x^2}) \, dx \quad -1 < x < 1$, and $y(0) = 0.$ If $\int_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1 - x^2} \, y(x) \, dx = k$ then $k^{−1}$ is equal to_______.

A copper block of mass 5.0 kg is heated to a temperature of 500°C and is placed on a large ice block. What is the maximum amount of ice that can melt?

[Specific heat of copper 0.39 J g^–1 °C^–1 and latent heat of fusion of water : 335 J g^–1]

$\begin{array}{l}\displaystyle \lim_{ x\to 0}\left(\frac{(x+2\cos x)^3 + 2(x+2\cos x)^2 + 3 \sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} \end{array}$

is equal to _________.

A parallel beam of light of wavelength $900 \,nm$ and intensity $100 \,Wm ^{-2}$ is incident on a surface perpendicular to the beam Tire number of photons crossing $1 \,cm ^2$ area perpendicular to the beam in one second is :

A parallel plate capacitor having cross-sectional area ‘A’ and separated by distance ‘d’ is filled by a copper plate of thickness b. its capacitance is :

If the potential at A is greater than the potential at B, then the equivalent resistance of the circuit across AB is

Which of the following graph correctly represents the variation of resistivity ‘s’ the temperature ‘T’ for a semiconductor material?

In a resonance column, the first and second resonance are obtained at depths 24 cm and 78 cm. The third resonance will be obtained at what depth?

In the following circuit, the equivalent resistance between X and Y is ...... $ \Omega $:

For an insulator, the forbidden energy gap is:

In the circuit shown in the figure, the AC source gives a voltage $ V = 20\cos(2000t) $. Neglecting source resistance, the voltmeter and ammeter readings will be:

The recoil speed of a hydrogen atom after it goes from $ n = 5 $ state to $ n = 1 $ state will be: